🤖 AI Summary
This study addresses the challenge of controlling bias and variance in estimating high-dimensional two-way fixed effects regression models under sparse bipartite networks. To this end, the authors propose a ridge regression–based regularization approach that stabilizes the estimation of fixed effect vectors by setting the regularization parameter to grow logarithmically with network size. Theoretical analysis demonstrates that both the bias and the covariance matrix of the proposed estimator converge to deterministic equivalents determined solely by the expected network structure. By integrating concentration inequalities, high-dimensional statistical inference, and sparse network modeling techniques, the work establishes the asymptotic properties of the estimator and validates its effectiveness and robustness through extensive simulations and empirical analysis using real administrative wage data.
📝 Abstract
We study a ridge estimator for the high-dimensional two-way fixed effect regression model with a sparse bipartite network. We develop concentration inequalities showing that when the ridge parameters increase as the log of the network size, the bias, and the variance-covariance matrix of the vector of estimated fixed effects converge to deterministic equivalents that depend only on the expected network. We provide simulations and an application using administrative data on wages for worker-firm matches.